We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its
L2 integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.
We investigate the generation and control of both charge and spin currents via nonreciprocal dissipative mechanisms in a two-dimensional spinful fermionic atom quantum system with broken inversion and time-reversal symmetries. Within the Gorini-Kossakowski-Sudarshan-Lindblad master equation formalism and using an approach based on the time-dependent generalized Gibbs ensemble, we identify in the weak dissipative coupling regime the minimal set of nonreciprocal jump operators required to induce charge and spin currents and to control both their direction and magnitude. We find that in the presence of finite tunneling, Rashba coupling and magnetic field, the combine application of two jump operators nonreciprocally coupling each spin species to a different spatial direction of motion is sufficient to generate both types of current. Furthermore, by tuning the degree of nonreciprocity of the jump operators we modify the dominant transport mechanism from spin to charge. Finally, we checked that this nonreciprocal current generation mechanism is robust to the application of dephasing noise as even in the presence of this additional dissipative process the steady-state occupation distributions for the quasiparticle modes of the Hamiltonian remains non-trivial, an essential requirement to obtain non-zero currents.
We study how translationally invariant couplings between many-particle systems and nonequilibrium baths can be used to rectify particle currents, for which we consider minimal setups to realize bath-induced currents in nonequilibrium steady states of one-dimensional open fermionic systems.We first analyze dissipative dynamics associated with a nonreciprocal Lindblad operator and identify a class of Lindblad operators that are sufficient to acquire a unidirectional current.We show that unidirectional particle transport can, in general, occur when a Lindblad operator is reciprocal provided that the inversion symmetry and the time-reversal symmetry of the microscopic Hamiltonian are broken.We demonstrate this mechanism on the basis of both analytical and numerical approaches, including the Rashba spin-orbit coupling and the Zeeman magnetic field.
The formal time symmetry of the quantum measurement process is extensively discussed. Then, the origin of the alleged association between a fixed temporal direction and quantum measurements is investigated. It is shown that some features of such an association might arise from epistemological rather than purely physical assumptions. In particular, it is brought out that a sequence of statements bearing on quantum measurements may display intrinsic asymmetric properties, irrespective of the location of corresponding measurements in time t of the Schrödinger equation. The situation of an observer performing two measurements in two opposite directions of t is eventually investigated. Essential differences are found between two descriptions of this situation: the internal one (taking only into account what is recorded in the observer's memory) and the external one (whereby the observer is considered as a quantum system ruled by the Schrödinger equation). Finally, a method allowing several observers to establish a correspondence between their memory sizes is analyzed. The most important facts that usually lead to the associating of a preferential temporal direction with quantum measurements may be inferred from this correspondence.
Owning to their high controllability, laser pulses have contributed greatly to our understanding of strongly correlated electron systems. However, typical multicycle pulses do not control the symmetry of systems, which plays an important role in the emergence of novel quantum phases. Here, we demonstrate that subcycle pulses whose oscillation is less than one period within a pulse envelope can control inversion and time-reversal symmetries in the electronic states of the one-dimensional extended Hubbard model. Using an ultrashort subcycle pulse, one can generate a steady electric current (SEC) in a photoexcited state due to an Aharonov-Bohm flux instantaneously introduced through the phase of an electric field. Consequently, time-reversal symmetry is broken. In contrast, a broad subcycle pulse does not induce SEC but instead generates electric polarization, thus breaking inversion symmetry. Both symmetry breakings in a photoexcited state can be monitored by second-harmonic generation. These findings provide a new methodology for designing the symmetries of electronic states and open up a new field of subcycle-pulse engineering.
We investigate the role of the global driving phase
Φ in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with closed-loop couplings, where external driving fields induce interference effects that strongly influence population transfer and symmetry properties of time-evolution. While full time-reversal symmetry requires
Φ=0,π, leading to a real Hamiltonian, we focus on a less restrictive transformation, the phase inversion (or complex conjugation of the Hamiltonian), under which population dynamics can remain symmetric even though coherences generally do not. We show that the presence of a dark (spectator) state is a sufficient condition for this population phase symmetry (P
ΦS), as it constrains the dynamics to reduced subspaces characterized by SU(2) or open-loop SU(3) evolution. We analyze this mechanism in three- and four-level systems and derive general conditions for P
ΦS that extend to generic
n-level configurations, with
n even. These findings provide practical guidelines for achieving robust control in quantum systems, with potential applications in quantum information processing and quantum computing.